How many positive are integer $x$ are there such that $3 x$ has $3$ digits and $4 x$ has $4$ digits?

Open in App

Solution

If $3 x$ is $3$ digit number, then
$\Rightarrow 99 < 3 x < 1000 \Rightarrow 33 < x \leq 333$
and $4 x$ is 4 digit number
$\Rightarrow 999 < 4 x < 10000 \Rightarrow 250 \leq x < 2500$
Thus $250 \leq x \leq 333$
Total number of integers $= 84$ .

Suggest Corrections

Similar questions

How many positive integers are there with distinct digits??

Q. How many such pairs of digits are there in the number 531468 each of which has as many digits between them in the number as when the digits are rearranged in descending order within the number?

Q. How many such pairs of digits are there in the number 254983 each of which has as many digits between them in the number as when the digits are rearranged in descending order within the number ?

How many such pairs of digits are there in the number 132546798 each of which has as many digits between them in the number as when they are arranged in ascending order?

Q. How many such pairs of digits are there in the number

98314625

, each of which has as many digits between them in the number, as when they are arranged in ascending order?

Join BYJU'S Learning Program

How many positive are integer x are there such that 3x has 3 digits and 4x has 4 digits?

If 3x is 3 digit number, then ⇒99<3x<1000⇒33<x≤333and 4x is 4 digit number⇒999<4x<10000⇒250≤x<2500Thus 250≤x≤333Total number of integers =84.

How many positive are integer $x$ are there such that $3 x$ has $3$ digits and $4 x$ has $4$ digits?

If $3 x$ is $3$ digit number, then
$\Rightarrow 99 < 3 x < 1000 \Rightarrow 33 < x \leq 333$
and $4 x$ is 4 digit number
$\Rightarrow 999 < 4 x < 10000 \Rightarrow 250 \leq x < 2500$
Thus $250 \leq x \leq 333$
Total number of integers $= 84$ .